How auction theory took the Nobel memorial prize in economics

12th November, 2020

If you and I were to bid against each other in a charity auction for, say, dinner with Princess Marie of Denmark, little would have to be explained about how the details of the auction work. One of us values the prospect more, would pay more, and would win.

But if you and I were bidding against each other for the joint value of the cash in our wallets, the auction becomes far more intriguing. I know only what is in my wallet and you know only what is in yours. Each of us should take a keen interest in what the other is willing to pay, since it is a clear signal of the value of the prize.

The charity auction for an evening with Princess Marie would be described by an economist as a private value auction. I have my own idea of its value, you have yours and the only question is whose value — and thus whose bid — is higher.

The wallet auction is known as a common value auction. The cash in the wallets is worth the same to each of us. To add to the intrigue, each of us has a piece of the puzzle but neither of us know everything about the true value.

This is a hint of the complexities involved in the ostensibly simple process of running an auction, or bidding in one. Auctions date back a long time. Almost 2,500 years ago, the historian Herodotus described men bidding for the most attractive wives in Babylon. Auctions also appear in Edward Gibbon’s The History of the Decline and Fall of the Roman Empire, as well as in Samuel Pepys’s diaries. Presumably, the auction is almost as old as the marketplace itself. It was no doubt invented many times over in markets when some buyer offered to pay four denarii per jar for fresh honey, and the man next to him said, “don’t settle for that price — I’ll give you five”.

The economist William Vickrey shared a Nobel memorial prize in 1996 in part for his foundational work on the theory of auctions. But Vickrey’s work, while elegant to the point of beauty, does not give economists the tools to analyse the complex practical auction design problems that real world settings require.

Into the breach stepped Robert Wilson and his former student Paul Milgrom, the Stanford professors who have shared the 2020 Nobel memorial prize in economic sciences “for improvements to auction theory and inventions of new auction formats”.

Paul Klemperer, a leading auction theorist at Oxford University, says that even the Nobel citation is hardly praise enough. “These were not just ‘improvements’. Robert Wilson is the father of practical auction design,” he said, “and Paul Milgrom could easily have won a second Nobel Prize for his work on the economics of information”.

Beyond the beauty of auction theory, the reason this matters is that governments have turned to auctions over the past few decades to allocate resources including logging rights, mineral exploration rights and the rights to use particular frequencies of radio spectrum for television or mobile phones. The alternative — handing out the resources cheaply to whoever spins the most plausible story — offers some conveniences to both buyers and politicians but is hardly in the public interest.

A well-designed auction forces bidders to reveal the truth about their own estimate of the prize’s value. At the same time, the auction shares that information with the other bidders. And it sets the price accordingly. It is quite a trick.

But in practice it is a difficult trick to get right. In the 1990s, the US Federal government turned to auction theorists — Milgrom and Wilson prominent among them — for advice on auctioning radio-spectrum rights.

“The theory that we had in place had only a little bit to do with the problems that they actually faced,” Milgrom recalled in an interview in 2007. “But the proposals that were being made by the government were proposals that we were perfectly capable of analysing the flaws in and improving.”

The basic challenge with radio-spectrum auctions is that many prizes are on offer, and bidders desire only certain combinations. A TV company might want the right to use Band A, or Band B, but not both. Or the right to broadcast in the east of England, but only if they also had the right to broadcast in the west. Such combinatorial auctions are formidably challenging to design, but Milgrom and Wilson got to work.

Joshua Gans, a former student of Milgrom’s who is now a professor at the University of Toronto, praises both men for their practicality. Their theoretical work is impressive, he said, “but they realised that when the world got too complex, they shouldn’t adhere to proving strict theorems”.

The peak of the excitement around spectrum auctions came at the turn of the century, when European countries auctioned spectrum rights at the height of dotcom mania. But auctions continue to be used to allocate scarce resources, and there is ample room to use them in future — for example, allocating the rights to fly to hub airports or the right to emit carbon dioxide, deciding which environmental projects should receive subsidies, or providing central bank loans to the banking system in times of stress.

Spectrum auctions have already raised many billions of dollars across the world; Milgrom, Wilson and another auction designer, Preston McAfee, were awarded a Golden Goose Award in 2014 — the award celebrates apparently obscure research which yields large social benefits.

And it is not just governments who use auctions. Every time you type a search term into Google, the advertisements you see alongside the results are there because they won a complex auction. Auctions helped to allocate the infrastructure on which the internet runs. Now they help to allocate our attention.

Written for and first published in the Financial Times on 12 October 2020.

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